On the anisotropic advection-diffusion equation with time dependent coefficients
Abstract
The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlation functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media
- Authors:
-
- UNAM (Mexico)
- Instituto Mexicano de Petroleo (Mexico)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1333060
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Revista Mexicana de Fisica
- Additional Journal Information:
- Journal Volume: 63; Journal Issue: 1; Journal ID: ISSN 0035-001X
- Publisher:
- Sociedad Mexicana de Physica
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; time-dependent diffusion; anisotropic media; tracer and pollutant transport
Citation Formats
Hernandez-Coronado, Hector, Coronado, Manuel, and Del-Castillo-Negrete, Diego B. On the anisotropic advection-diffusion equation with time dependent coefficients. United States: N. p., 2017.
Web.
Hernandez-Coronado, Hector, Coronado, Manuel, & Del-Castillo-Negrete, Diego B. On the anisotropic advection-diffusion equation with time dependent coefficients. United States.
Hernandez-Coronado, Hector, Coronado, Manuel, and Del-Castillo-Negrete, Diego B. 2017.
"On the anisotropic advection-diffusion equation with time dependent coefficients". United States. https://www.osti.gov/servlets/purl/1333060.
@article{osti_1333060,
title = {On the anisotropic advection-diffusion equation with time dependent coefficients},
author = {Hernandez-Coronado, Hector and Coronado, Manuel and Del-Castillo-Negrete, Diego B.},
abstractNote = {The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlation functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media},
doi = {},
url = {https://www.osti.gov/biblio/1333060},
journal = {Revista Mexicana de Fisica},
issn = {0035-001X},
number = 1,
volume = 63,
place = {United States},
year = {Wed Feb 01 00:00:00 EST 2017},
month = {Wed Feb 01 00:00:00 EST 2017}
}